*Review* **A Comprehensive Review of Lithium-Ion Cell Temperature Estimation Techniques Applicable to Health-Conscious Fast Charging and Smart Battery Management Systems**

**Akash Samanta 1,\* and Sheldon S. Williamson <sup>2</sup>**


**Abstract:** Highly nonlinear characteristics of lithium-ion batteries (LIBs) are significantly influenced by the external and internal temperature of the LIB cell. Moreover, a cell temperature beyond the manufacturer's specified safe operating limit could lead to thermal runaway and even fire hazards and safety concerns to operating personnel. Therefore, accurate information of cell internal and surface temperature of LIB is highly crucial for effective thermal management and proper operation of a battery management system (BMS). Accurate temperature information is also essential to BMS for the accurate estimation of various important states of LIB, such as state of charge, state of health and so on. High-capacity LIB packs, used in electric vehicles and grid-tied stationary energy storage system essentially consist of thousands of individual LIB cells. Therefore, installing a physical sensor at each cell, especially at the cell core, is not practically feasible from the solution cost, space and weight point of view. A solution is to develop a suitable estimation strategy which led scholars to propose different temperature estimation schemes aiming to establish a balance among accuracy, adaptability, modelling complexity and computational cost. This article presented an exhaustive review of these estimation strategies covering recent developments, current issues, major challenges, and future research recommendations. The prime intention is to provide a detailed guideline to researchers and industries towards developing a highly accurate, intelligent, adaptive, easy-to-implement and computationally efficient online temperature estimation strategy applicable to health-conscious fast charging and smart onboard BMS.

**Keywords:** electric vehicles; machine learning; Kalman filter; thermal modelling; online prediction; electromagnetic impedance spectroscopy; computational cost

#### **1. Introduction**

Lithium-ion batteries (LIBs) are widely used in electric vehicles (EVs), grid-tied stationary energy storage systems, and several other consumer electronics primarily due to their high voltage rating (>4 V/cell) and high energy density (~265 (W h) L−1) and longer operational life. The use of LIBs in automotive and aerospace applications has led to larger cell sizes and large battery packs for a higher driving range and the requirement for more aggressive charging and discharging. However, thermal instability and temperaturedependent nonlinear behavior is some of the common concerns behind the safe and reliable operation of LIB systems. It is noticed that the operation of batteries outside the safe operating temperature directly affects the performance of LIBs, such as cycle life, efficiency, reliability and safety. Researchers investigating the thermal performance of LIB showed that the best operating temperature range is from 25 ◦C to 40 ◦C [1,2]. Richardson et al. [3] demonstrated that the difference between the core and surface temperature could reach more than 10 ◦C during real-life applications, especially during the high discharging condition and fluctuating load current demand. The excessive temperature difference and the

**Citation:** Samanta, A.; Williamson, S.S. A Comprehensive Review of Lithium-Ion Cell Temperature Estimation Techniques Applicable to Health-Conscious Fast Charging and Smart Battery Management Systems. *Energies* **2021**, *14*, 5960. https:// doi.org/10.3390/en14185960

Academic Editors: Andrei Blinov, Sheldon Williamson, Seung-Wan Song and Mario Marchesoni

Received: 5 July 2021 Accepted: 13 September 2021 Published: 20 September 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

accumulation of a large amount of heat inside the cell could lead to thermal runaway or even explosions and fire [4]. That necessitates the employment of a battery management system (BMS) for effective monitoring of battery parameters (current, voltage, temperature), estimation of battery states (state of charge (SOC), state of health (SOH), remaining useful life (RUL), state of temperature (SOT) [5]). Research studies demonstrated that SOC [6], SOH [7], and remaining storage capacity [8] are a function of temperature; thus, the estimation of the battery states also depends on the accurate estimation of cell temperature. The Columbic efficiency of a cell is greatly affected by the cell temperature during the charging and discharging period. Few other popular functionalities of BMS include cell balancing [9] and fault detection/diagnosis [10] to ensure optimum capacity utilization, operational safety, reliability, and longer battery life often requires temperature information of an individual cell and battery pack as well. Therefore, accurate information of core and surface temperature is highly crucial for effective thermal management and safety of a LIB pack. Moreover, in cold climate areas, the battery capacity is drastically reduced due to low-temperature operation that requires preheating the battery to a suitable range for optimum performance [11,12]. It is also evidenced that for every 0.1 ◦C beyond the safe operating region the battery capacity degrades by about 5% [13]. It is evidenced that maximum heat is generated during the discharging period especially with fast discharging [14]. Therefore, accurate temperature estimation is essential for effective thermal management and safety during fast charging and discharging and preheating of the cell to minimize capacity fade.

In summary, it could be stated that the accurate information of cell temperature is undoubtedly serving as the essential basis for the thermal management and safety of LIB. While the surface temperature of each cell can be measured by installing a temperature sensor on each cell, the core or internal temperature measurement directly using physical sensors is challenging. Moreover, installing a temperature sensor on each cell surface is not practically feasible from a system cost, space and weight point of view as any high-capacity battery pack used in EVs and grid-tied systems essentially consists of thousands of individual cells. Researchers have also incorporated multi-dimensional sensing and self-healing functions into a single battery cell to develop a smart battery [15–18]. Smart cells are typically capable of parameter measurements and estimation of cell states including the state of temperature. Despite the modularized application of BMS in smart batteries, accurate temperature estimation is still required, as otherwise installing sensors in each cell results in high implementation cost and complexity. Therefore, researchers are struggling hard to develop a high-fidelity, accurate, easy-to-implement, and computationally inexpensive online temperature estimation strategy suitable for low-cost onboard BMS. Several temperature estimation techniques have been proposed by researchers so far. Each different type of method has its advantages and limitations with respect to the above-mentioned features of an optimum BMS. Therefore, a summary of all the prominent techniques would be very helpful to researchers and developers serving as a baseline for further research and as a guideline for selecting appropriate techniques suitable for a specific requirement. However, such a summary with detailed discussion on current progress and explanation of the existing issues, challenges and future research scopes has not yet been presented in the literature. Therefore, this article covered the research gap by conducting a comprehensive review of the state-of-the-art temperature estimation strategies reported in the literature so far.

The paper is organized as follows: In Section 2, generic temperature estimation strategy of LIB is presented. The classification of temperature estimation strategies is presented in Section 3. Section 4 is dedicated to presenting the existing estimation techniques, their evolutions, limitations and challenges. It should be noted that temperature estimation strategies for LIBs reported in the literature between 2010 to 2021 are primarily considered. However, few prominent research articles published between 1990 to 2010 are also considered for understanding the fundamentals and evolution of temperature estimation schemes. Commonly used search platforms, such as "Google Scholar", "Science Direct", and IEEE Xplore, were used to find research articles published within this tenure. The search criteria were "Temperature Estimation of Lithium-ion Batteries". Section 5 discusses the current issues, challenges and future research recommendations. Finally, Section 6 is dedicated to a summary of the major findings and concluding remarks.

#### **2. Generic Temperature Estimation Strategy**

Irrespective of battery chemistry, heat is accumulated inside the battery during the charging/discharging even during idle conditions, majorly due to several largely exothermic chemical and electrochemical reactions as well as transport processes. If the heat transfer from the battery to the surroundings is not sufficient, then the heat gets accumulated inside the battery resulting in an increase in core and surface temperature, thereby risking thermal runaway. This phenomenon is even more prominent in the case of hard-cased insulated batteries (as used in EVs), under fast charging/discharging and the operation in hot environments. Heat dissipation is worse in cylindrical LIBs that are extensively used in high-capacity LIB packs. Therefore, a typical temperature estimation scheme consists of two models, namely, a heat generation model and a heat transfer model [19]. Often, a battery electrical model is also used to estimate the total heat generation using Bernardi's [20] heat generation model whereas few other models use a mathematical form of battery electrochemistry to calculate the heat generation. Adaptive estimation strategies also consider the influence of different battery states, such as SOC and SOH, as the battery temperature is a function of these battery states. Then, the heat transfer model takes the estimated total heat quantity as well as few other external measurements such as ambient temperature to predict the temperature of that cell. Closed-loop estimation schemes use the measured or the estimation temperature as feedback to improve the prediction accuracy. A schematic layout of a generic temperature estimation strategy for LIB is shown in Figure 1.

**Figure 1.** Schematic layout of a generic temperature estimation strategy for a LIB cell.

#### **3. Classification of Temperature Estimation Strategies**

As shown in Figure 1, typically, a temperature estimation scheme consists of a heat generation model and a heat transfer model. The heat generation models reported in the literature can be broadly classified from two different aspects; based on modelling strategy and based on the source of heat generation. Heat generation models based on modelling strategy can be classified into three groups, physics-based electrochemical models [21–24], equivalent circuit models (ECM) [25–27], black-box models [28–30]. In contrast, based on the source of heat generation, these models can be grouped as a concentrated model, distributed model [31] and heterogeneous model [25,32]. The concentrated heat generation model considers that all heat is generated at the core only, usually considered to reduce the modelling complexity. The distributed heat generation model considers that uniform heat is generated throughout the entire cell geometry whereas the heterogeneous model can capture different heat generation from difference cell layers usually resulting in temperature and current density gradients inside the cell. The heterogeneous models are more detailed thus can produce highly accurate predictions; however, these are most complex and require extensive experiments for modelling. Distributed heat generation models are a balance

between the concentrated and heterogeneous models. The heat transfer models can be classified into finite element analysis (FEA)-based models [27,33–36], heat capacitor-resistor models (lumped or distributed parameter) [28,37–40], and data-driven techniques. Heat capacitor–resistor-based models use the analogy between electrical and thermal systems. A heat capacitor–resistor can be further classified as mentioned in Figure 2. Lumped parameter models are simple and useful for online applications, however, only one or two average temperatures can be predicted with these models whilst the battery temperature distribution is not spatially uniform, especially in larger capacity cylindrical LIB cells. On the other hand, complex distributed models [41,42] can describe the detailed temperature distribution in a cell, however, they are not suitable for online application due to their computational complexity. Several other detailed models of LIB accounting for the thermal characteristics of different layers are studied in [43–48]. A two-state/node model provides information on core and surface temperature whereas a one-state/node model can provide only core temperature.

**Figure 2.** Family of (**A**) Heat generation model, (**B**) Heat transfer model, (**C**) Temperature estimation strategy.

The heat transfer model where the total heat generation is one of the input parameters is collectively called the battery thermal model where the total heat generation is estimated by the battery heat generation model. The thermal modelling of LIB is a separate area of study and is not under the scope of this study. It deals only with the temperature estimation strategies. However, as most of the temperature estimation strategies are extensively depending on thermal modelling, an overview of each modelling technique is also discussed with the respective temperature estimation strategy for better understanding. Researchers employed different types of heat generation models with different kinds of heat transfer models to come up with a temperature estimation scheme. Therefore, it is challenging to classify these estimation strategies. Broadly, the temperature estimation schemes can be grouped into electrochemical thermal modelling-based, equivalent electric circuit model (EECM)-based, machine learning (ML)-based, numerical-model based, direct impedance measurement-based, magnetic nanoparticles-based schemes. The families of the LIB heat generation model, heat transfer model and temperature estimation strategy are illustrated in Figure 2.

#### **4. Comprehensive Review of Temperature Estimation Strategies**

*4.1. Electrochemical Thermal Modelling-Based Temperature Estimation*

Researchers started thermal modelling in the early nineties, those are mostly coupled with an electrochemical model to simulate the temperature profile of a battery under different operating conditions, geometries or cooling rates. There are simple one-dimensional (radial direction) models [37,49–54] to complex three-dimensional thermal models [55–59]. Researchers have primarily used different analytical techniques to mathematically model the electrochemical behavior of the cell. One-dimensional models typically assume isothermal, constant current operation of the battery and lumped thermophysical properties and constant heat generation rates. Highly complex three-dimensional models require an in-depth understanding of the thermodynamic properties of battery materials and parts to consider the heat effects caused by ohmic resistance, chemical reactions, mixing processes, polarization and electrode kinetic resistance. Often, temperature estimation using such highly complex models is very accurate, however, such detailed models are essential for battery design purposes. Those are not compatible with temperature estimation using onboard BMS with low computational resources. These complex models are capable of accounting for the time-varying nonlinear battery performance. However, they typically require several system properties, operational parameters which require extensive experimental measurements. While, at the same time, quantitative estimation of some of the properties, such as transport properties, thermodynamic properties and heat effects are highly challenging.

Thomas and Newman [60] introduced an electrochemical modelling-based detailed heat generation model of LIB to estimate the total heat generation during the charging/discharging period. The fundamental equation of the total heat generation inside the LIB cell as proposed by Thomas and Newman reads

$$Q = I(V - \mathcal{U}^{avg}) + IT\frac{\partial \mathcal{U}^{avg}}{\partial T} - \sum\_{i} \Delta H\_{i}^{avg} r\_{i} - \int \sum\_{j} (\overline{H}\_{j} - \overline{H}\_{j}^{avg}) \frac{\partial \mathcal{C}\_{j}}{\partial t} dv \tag{1}$$

In Equation (1), *Q* is the rate of heat generated or consumed inside the cell, *V* and *U* are the cell voltage and equilibrium potential, respectively, *I* is the charging or discharging current, *T* is the cell temperature. Δ*Hi* represents the changes in enthalpy of the chemical reaction i and *ri* is the rate of reaction i. Δ*Hj* represents the partial molar enthalpy of species j and *cj* is the concentration of the species. *t* and *v* represent the time and volume of the cell, respectively. All the properties are mentioned based on the volume-averaged concentration, thus the superscript "*avg*" is used. The model can provide accurate information on heat generation only, temperature estimation is not presented in this study. Their heat generation model was extensively used by several other researchers. Modelling is very detailed thus highly complicated and not suitable for online application owing to the computational burden. One of the widely-used electrochemical models commonly known as the Doyle–Fuller–Newmann model [37,61] is extensively referred to and also used for thermal modelling. It consists of nonlinear partial differential-algebraic equations to describe the internal characteristics of LIB. It is also referred to as the pseudo-twodimensional (P2D) model. The major limitation of the model is its high computational burden which limits its application in online state estimation in embedded BMSs. Here,

Al Hallaj et al. [53] showed that a simplified transient one-dimensional thermal model with lumped parameters is sufficient for cell design purposes, especially to simulate the thermal behavior of scaled-up LIBs. Detailed knowledge of the role of different cell components, such as electrodes, electrolytes and separators in heat generation is also not necessary. Few researchers used this type of complex electrochemical model to explore pulse power limitations to prevent thermal runaway and to design thermal management systems [62,63]. Those are mostly used for designing LIB cells as well as LIB packs. A lumped electrochemical-thermal-coupled model was used to predict the thermal performance of LIB alongside the performance of individual electrodes at various operating temperatures by Fang et al. [64]. The model was validated against the experimental data for constant current and pulsing conditions characteristic of hybrid electric vehicle (HEV) which are merely providing the laboratory experimental results instead of a real-work application scenario. The impact of charging current on internal temperature behavior was investigated in [65]. Gerver et al. [66] included more detailed information and cell characteristics to develop a multi-dimensional electrochemical thermal model of LIB to analyze the thermal performance and heat generation more accurately. Despite estimation accuracy, the modelling complexity and computational burden limit its application in embedded BMS.

Due to a lack of clear understanding of the electrochemical processes inside the LIB and their corresponding mathematical equations alongside to reduce the computational expenses, often all heat generation sources were not modelled/considered. These unmodeled heat generation behaviors lead to significant errors in temperature estimation. Regarding this, Zhang et al. [67] developed a two-state thermal model utilizing discretization and inverse model techniques which do not require prior knowledge of thermal boundary conditions. Moreover, the model is capable of estimating the total heat generation of a battery cell, thus, thermal modelling of each heat source is not required and abnormal heat generation can also be detected from the estimation results. The effectiveness and robustness of the model were tested for varying thermal boundary conditions and fast charging conditions. While the strategy is designed for self-heating pouch cells, a similar approach could also be adapted for other types of LIBs. Thus, further research is recommended here. A high-fidelity electrochemical model and onboard measurements such as terminal voltage and current were used by Wang et al. [68] to estimate the cell temperature at a wide range of C-rates during the charging/discharging period. They have also used a dual ensemble Kalman filter (DEKF) which incorporates enhanced singleparticle dynamics to relate terminal voltage to battery temperature and Li+ concentration. Besides, modelling complexity and high computational cost, the accurate determination of lithium (Li+) concentration is challenging. Therefore, the application of the model in real-life online prediction is questionable. The spatial distribution of internal temperature in LIB was estimated using a pseudo-2D electrochemical model and soft-constrained dual unscented Kalman filter (DUKF) by Marelli and Corno [69]. It is mainly developed to estimate the Li+ concentration and modelling complexity and computational expenses are very high. However, the approach could be extended for temperature estimation. Smith et al. [62] developed a one-dimensional electrochemical, lumped thermal model to explore pulse power limitations and thermal behavior of a LIB pack. The electrochemical thermal modelling-based temperature estimation strategies proposed by different authors are summarized in Table 1 for a quick reference to the readers. In general, the major limitations of any electrochemical model-based strategies are the modelling complexity and high computational cost making these models unsuitable for online prediction and application at low-cost onboard BMS.


**Table 1.** Summary of electrochemical thermal modelling-based temperature estimation strategies.

#### *4.2. Equivalent Electric Circuit Model-Based Temperature Estimation*

An equivalent electric circuit model (EECM) represents the thermal dynamics of LIB using electrical system parameters to develop a heat capacitor–resistor-based battery thermal model. Depending on the number of heat capacitors (number of energy storage elements) two types of models, namely, the first-order model and second-order model have been developed so far in the literature. The first-order model consists of one thermal energy storage element whereas a second-order thermal model consists of two heat capacitors, typically, one for the heat capacitance of the core and the other one is for the cell surface [13]. The second-order model can capture more dynamics than the first-order model. The firstorder and second-order thermal models of a LIB cell are shown in Figure 3a,b, respectively. In Figure 3, *Q* represents the heat generation rate, *Cc* and *Cs* are the heat capacitance of core and surface, respectively, *Tin* and *Tout* are the temperatures of core and surface of the cell, respectively. *Tamb* is the ambient temperature.

**Figure 3.** Thermal model of a LIB cell (**a**) First-order model, (**b**) Second-order model.

Further, depending on the modelling complexity, EECM could be also classified as lumped-parameter and distributed parameter models. Lumped-parameter models are used for simplification and thus low computational cost compared to detailed distributed models. Computationally efficient lumped thermal models are developed using single temperature as input to capture the model parameters [70] while some researchers used both surface and core temperatures of the cell to construct the lumped thermal models. Some also considered the correlation between cell geometry and other physical properties with thermal modelling [71]. However, several assumptions were made during modelling leading to inaccurate temperature estimation compared to detailed thermal modelling. Further, thermal models that only estimate the core temperature are considered as singlestate/node [72], whereas if the model can estimate both surface and core temperature then it is termed as two-state/node [67] thermal model. The parameters of the EECM are identified through ranges of experimental studies such as electrochemical impedance spectroscopy (EIS) or utilizing externally measurable quantities, such as voltage, current, and temperature. Few studies also considered various conditions of SOC, SOH and estimated surface/core temperatures to make the model more robust. It is very difficult to group those thermal models because lumped models are used in both single-state and dual-state modelling and the model could be first-order and second-order. Therefore, the literature is grouped into cell-level and pack-level temperature estimation schemes that are discussed below.

Typically, these EECM models determine the value of *Q* using Equation (2) as formulated by Bernardi et al. [20]:

$$Q = I(V - V\_{OCV}) + IT\_c \frac{dV\_{ocv}}{dT\_c} \tag{2}$$

where *Vocv* represents the open-circuit voltage of the battery cell and the term *dVocv dTc* is the entropy coefficient. Finally, *Tc* and *Ts* are estimated using the mathematical form of the thermal models shown in Figure 3. Mathematical equations for temperature estimation using the firstorder and second-order thermal model are represented by Equations (3) and (4), respectively.

#### 4.2.1. EECM-Based Cell Temperature Estimation

One of the prime challenges of any EECM-based strategy is model parameter identification. Forgeze et al. [43] used transient experiments by applying current pulses of different magnitudes to increase the internal temperature and the model parameters, heat transfer coefficients and heat capacity were determined to construct a lumped parameter thermal model. This study used EIS for parameter identification where current pulses at 2 Hz were used to increase the internal temperature. The *Tc* was estimated based on the measured surface temperature using the lumped parameter thermal model. The entropy change was also taken into account while modelling. They developed a first-order thermal

model as shown in Figure 3a. The mathematical representation of the first-order thermal model as used by Forgeze et al. reads

$$T\_{\rm in} = T\_s \left( 1 + \frac{R\_{\rm in}}{R\_{\rm out}} \right) - \ T\_{\rm amb} \frac{R\_{\rm in}}{R\_{\rm out}} \tag{3}$$

The strategy developed by Forgez et al. lacks quantitative analysis of the influence of heat generation. The operating current is much higher compared to the very low current value used in EIS. Therefore, model parameters determined using EIS are not appropriate for capturing the thermal dynamics accurately. Moreover, they have considered uniform internal temperature, however, more than 10 ◦C temperature difference among different internal points of a cell has been reported in the same study. This strategy requires surface temperature measurement by installing a temperature sensor at each cell, thus scaling-up is impractical. Maleki and Shamsuri [73] developed a thermal model of notebook computer LIB-pack to understand the thermal response under various operating conditions aiming to reduce the battery pack designing cost and time. They revealed that the temperature rise during charging is dominated by heat dissipation from the control power electronics while during discharging it is dominated by the heat generated inside the LIB cell. These relevant observations must be considered while designing an effective thermal management system of LIB pack, especially for health-conscious fast charging. Surya et al. [13] developed a second-order thermal model for core and surface temperature estimation scheme using KF. Here, the least square (LS) algorithm was employed to identify the battery thermal parameters. Despite the simplicity and good accuracy, environmental uncertainties were not considered during modelling. Moreover, they presented the results based on simulation study alongside very simple and low-current discharge profile was used for model validation, thus, the accuracy in the real-world applications needs further investigation. Previously, models were validated using a simple charging/discharging current profile. However, the load profile in real-life applications much deviates from those simple loading profiles. Therefore, a second-order thermal model and ECM-based two-state thermal model of cylindrical LIB cell were validated with two basic drive-cycle tests, covering an SOC range 25–100%, temperature 5–38 ◦C, and maximum C-rate of 22 by Lin et al. [74]. The influence of the constantly varying temperature and SOC on the EECM parameters and consequential effect on battery thermal performance was investigated by Lin et al. [74]. The model demonstrated good prediction accuracy and robustness. However, testing using standard internationally referred drive-cycles was not conducted. Thus, accuracy and robustness in practical scenarios need further investigation. EECM parameters are influenced by cell ageing, thus, Li and Yang [75] considered the influences of ageing and heat transfer conditions on thermophysical model parameters. Li and Yang identified the parameters of the extended lumped parameter model online where a forgetting factor recursive least squares (FFRLS) algorithm was employed.

Further to this research, the uncertainties in practical operation were considered by Lin et al. [45,76] alongside the impact of cell ageing during online parameter identification. As an up-gradation, the commonly deployed LS algorithm was augmented with nonuniform forgetting factors to track the time-varying internal parameters making the model adaptive to cell ageing and other uncertainties. In [77], only two lumped models were used to approximate the core and surface temperatures, respectively, which may not be suitable for a large capacity LIB pack due to strong spatiotemporal thermal distribution. While the influence of overpotential entropy changes on battery heat generation was considered, core temperatures estimation of only a single cell was considered. Sun et al. [78] developed a second-order lumped parameter thermal model with the KF technique for core temperature estimation only (single-state). They used an ECM-based heat generation model to mathematically model the accumulation of the total heat generation at the cell core. As an improvement of previous studies, this study considered the influence of entropy changes and overpotential on cell thermal behavior and was quantitively analyzed to develop an online internal temperature estimation strategy. This strategy utilized surface

and ambient temperature for core temperature estimation during charge and discharge cycles where the KF was used for adaptive estimation by the process of state and time update in real-time. The impact of unmeasurable modelling error, the initialization error and the possible time-varying external thermal resistance on the temperature estimation accuracy were considered by Dai et al. [79]. In that paper, a second-order lumped parameter thermal model, as shown in Figure 3b, was developed for adaptive core temperature estimation based on the KF. Further, joint Kalman filtering (JKF) was used to simultaneously estimate both core temperature and time-varying external thermal resistance online. The mathematical equation employed by Dai et al. for core temperature estimation can be represented as Equation (4):

$$T\_{in}(s) = \frac{\left(1 + \frac{R\_{in}}{R\_{out}} + C\_s R\_{in} s\right)}{C\_s C\_c s^2 + \left(C\_s + C\_c + \frac{R\_{in} C\_c}{R\_{out}}\right) s + \frac{1}{R\_{out}}} Q(s) \tag{4}$$

where *s* is the Laplace operator. Other parameters are the same as mentioned in Figure 3.

The LS algorithm based on the experimental data was also used to determine the lumped parameters of the thermal model. Dai et al. enhanced the modelling accuracy by constructing a separate thermal model for core and battery shell alongside considering the external heat exchange coefficient as time-varying. The authors simply stated that the proposed method computes efficiently, however, no information about computation time, hardware requirement was presented. Several assumptions were also made during modelling, leading to inaccurate estimation in real-life applications.

A trade-off between the detailed and lumped parameter thermal modelling approaches was considered by Doughty et al. [80] and Park et al. [71]. They developed a two-state thermal model that predicts the surface and core temperature of LIB. The novel intention was to provide more information compared to the lumped model while reducing the computational cost. Few researchers also termed the lumped parameter model as a reduced-order model (ROM). Whilst the primary intention is same, that is, to reduce the complex thermal problem into a simplified heat transfer problem characterized by a reduced set of thermal parameters. A combination of lumped parameter two-state thermal model with 2RC (second-order) ECM along with a joint Kalman filter (JKF)-based core and surface temperature estimation strategy was proposed by Chen et al. [72]. The simulation and experimental test were conducted to verify the adaptiveness of the model to constantly varying temperature and SOC and, finally, the prediction accuracy was also assessed. It was also demonstrated that the proposed model has higher prediction accuracy compared to previously discussed EECMs. It was also demonstrated that the model is highly robust against automatic correction for surface thermal resistance.

To provide more detailed information on the temperature distribution in cylindrical LIB, Xie et al. [81] developed a one-dimensional (radial) lumped parameter thermal model with a dual Kalman filter (DKF). As an improvement, this model is capable to provide temperature information at three different points of the battery, compared to only core and surface temperature. Thus, the researchers termed this modelling as a three-node thermal model. In this study, the anisotropy of thermal conductivity was also considered in identifying internal resistance and SOC during the temperature estimation to enhance the prediction accuracy and robustness. The impact of different charging/discharging current conditions was not considered. Moreover, 1-RC ECM-based heat generation model is considered, thus presumably, the accuracy can be further improved with the application of the 2-RC ECM-based heat generation model. Online parameter estimation using a particleswarm algorithm with pulse discharge experiments under different ambient temperatures was employed by Pan et al. [19]. A combination of 2RC ECM and a multi-node heat transfer model based on the battery geometry was employed in the study to obtain a more detailed temperature gradient inside the large prismatic LIB. The research showed that the hybrid model could provide similar results to the finite element method (FEM), however, the computational burden was reduced by around 90%. They also revealed that the cell

geometry has a strong influence on the cell temperature profile. Despite good accuracy, the effect of cell ageing and the effort of developing pack-level thermal modelling were not considered in this study.

The impact of heat dissipation through radiation from the surface of the cell was introduced in the thermal modelling of LIB by Sun et al. [82]. A lumped thermal model considering the radiation effect was then used for core temperature estimation with the help of an Extended Unscented Kalman Filter (EUKF). The sensor bias was augmented as an extended state to enhance the prediction accuracy and model robustness. While the load profile of residential energy storage was tested, the suitability in commercial vehicle applications was not tested. Further, model parameters were assumed to be constant irrespective of environmental uncertainties which may be in conflict with the facts when the operating conditions will vary significantly. Zhu et al. [83] developed a lumped twostate thermal-electrical model for estimating both the surface and the core temperatures where the thermal impact of the adjacent cell was also considered during modelling. Further, an extended state observer (ESO) with the feedback of the surface temperature was employed to address the model uncertainties and time-variant parameters in the estimation model. This approach is specifically designed for rapid self-heating of self-heating batteries. The concept of model-based virtual thermal sensors (VTS) was introduced by Xiao Y. [84] that combines the tuned thermal model with a KF observer along with an online parameteridentification algorithm for surface and core temperature estimation utilizing a single temperature sensor input. While the strategy is adaptive to environmental uncertainties, it still requires a sensor for feedback; thus, the strategy cannot be termed as completely sensorless. Despite that it minimizes the sensor requirement and enhances the model adaptability, the concept is similar to other lumped parameter EECM-based methods. The effect of fast-discharge on core temperature of LIB was demonstrated by Surya and Mn [14] where a combination of 1-RC ECM, single-state thermal model and KF was used for core temperate estimation. They used a recursive least square (RLS) algorithm to identify model thermal parameters. However, further research is recommended to develop health-conscious BMS suitable for fast charging/discharging.

#### 4.2.2. EECM-Based Temperature Estimation of LIB Pack

Most of the research studies covered only the temperature estimation of a single cell. Thermal modelling and temperature estimation of a LIB pack were seldomly reported. A ROM of a LIB pack considering the characteristic of the inner electrical resistance of the battery was used for core temperature estimation by Ma et al. [85]. Here, RLS was used for the thermal parameter identification. In this study, several assumptions were made while establishing ROM of a battery pack such that parameters of each cell are the same and the thermal behavior of each cell row is same. The heat transfer among cells via conduction through tabs and wires were neglected which could give rise to the error in temperature estimation. Thermal modelling of a LIB pack by scaling-up a single cell thermal model was investigated by Ismail et al. [86] using a simulation study. Considerable accuracy has been noticed, however, several assumptions were made to scale up the single-cell model to battery pack models, such as uniform cell characteristics, constant ambient conditions and 100% efficient discharging process that are far from the real-life scenario. Therefore, the accuracy of the temperature estimation strategy in real-world applications needs to be further explored. Therefore, from the above discussion, it can be stated that the pack-level estimation schemes need significant further research. The EECMbased temperature estimation strategies proposed by different authors are summarized in Table 2 for a quick reference to the readers. One of the major limitations of EECM-based temperature estimation techniques is the requirement of online sensor feedback. This is because the estimation accuracy is completely relying on accuracy of the knowledge of the cell thermal properties, heat generation rates, and thermal boundary conditions represented in terms of electrical parameters that are subjected to change due to cell aging, operating temperature and other practical uncertainties.


**Table 2.** Summary of EECM-based temperature estimation strategies.

#### *4.3. Numerical Analysis-Based Temperature Estimation*

Numerical method-based techniques were successfully implemented for temperature estimation of different chemistries and shapes of LIB cells and even LIB packs. So far, the finite element method (FEM) [87–90] and finite volume method (FVM) [91] were extensively used for temperature estimation. Numerical analysis-based techniques try to mathematically describe the thermal dynamics inside the battery using nonlinear partial differential equations (PDEs) such as used by Du et al. [89]. They have employed FEM analysis with a three-dimensional model and Bernardi equation-based internal heat generation rate. Typically, the PDEs have complex boundary conditions that are infinite-dimensional. The fundamental mathematical equation as employed by Du et al. can be represented as Equation (5)

$$
\rho C\_p \frac{\partial T}{\partial t} = \lambda\_x \frac{\partial^2 T}{\partial x^2} + \lambda\_y \frac{\delta^2 T}{\delta y^2} + \lambda\_z \frac{\delta^2 T}{\delta z^2} + Q \tag{5}
$$

where *ρ*, *Cp* represent the mean density and mean specific heat of the cell, respectively. *λ* is the heat conductivity coefficient of the surface material of the cell and *Q* is the same as in Equation (1).

Dong Hyup Jeon [87] incorporated a transient thermoelectric model with a porous electrode model and conducted a numerical simulation to understand the thermal behavior of a commercial LIB under charging and discharging conditions. He demonstrated that temperature increase during discharging is much higher compared to the temperature rise during charging. He also suggested that the temperature difference between charge and discharge can be decreased with increasing C-rates. Further, Baba et al. [88] conducted a numerical simulation of an enhanced single-particle model of a LIB to understand the three-dimensional temperature distribution inside the cell. Numerical analysis was used for transient behaviors of a LIB under a dynamic driving cycle by Yi et al. [90]. Doublelayer thermal capacitance was used to capture the short-term transient behavior of the LIB chemistry. Fleckenstein et al. [91] using FVM to demonstrate that the temperature gradients inside the cell layer result in different current densities and local SOC inhomogeneities in LIB. These phenomena must be well-taken care of while designing an effective thermal management system. In general, this kind of model is best for capturing both temporally and spatially thermal distribution of the cell as the battery thermal process is a typical distributed parameter system. Despite high accuracy and detailed information about cell temperature gradient, these numerical method-based temperature estimation strategies are not suitable for online temperature estimation due to high computational cost. The complex mathematical analysis also required expertise and strong domain knowledge. Moreover, generalization is not possible as different chemistry and cell physics affect mathematical modelling. A summary of numerical methods-based temperature estimation strategies is shown in Table 3.


**Table 3.** Summary of numerical methods-based temperature estimation strategies.


**Table 3.** *Cont.*

#### *4.4. Direct Impedance Measurement-Based Temperature Estimation*

Cell internal temperature estimation using a lumped-parameter thermal model and an approximate distributed thermal model have several drawbacks. Firstly, accurate determination of thermal model parameters such as heat generation and cell thermal properties is highly challenging. Heat generation inside the cell is typically approximated by measuring the cell operating current, voltage and the internal resistance that are again functions of SOC, cell internal temperature and SOH. Moreover, a cell is constructed using many different materials combined into a layered structure and thermal contact resistances between these layers are often unknown. Temperature estimation methods use surface temperature measurements and even the combination of surface-mounted temperature sensor and thermal model typically failed to detect the thermal runaway as rapid fluctuations in the internal temperature is difficult to capture using surface mounted sensors because the heat conduction between the core and battery surface takes a considerable amount of time [92]. Furthermore, embedding micro-temperature sensors within the cell [93,94] is not practically possible for a large capacity LIB pack from a manufacturing complexity and system cost point of view. Hence, the core temperature measurement using a physical sensor is not an appropriate method for industrial applications.

Srinivasan et al. [95,96] noticed that the phase of electrochemical impedance in the frequency range of 40 to 100 Hz is temperature-sensitive but insensitive to changes in other parameters such as SOC and SOH. Based on these findings, they demonstrated an electrochemical impedance-based cell internal temperature estimation strategy. However, they assumed the uniform internal temperature and the estimation method is only valid in the temperature range of from −20 to 66 ◦C. The temperature estimation considering the effect of temperature non-uniformity on electrochemical impedance was studied by Schmidt et al. [97] based on the principle derived by Troxler et al. [98]. Both the strategy developed by Srinivasan et al. and Schmidt et al. were only able to estimate the mean temperature of the cell, however, in real-life application, especially in the case of cylindrical battery under high charging/discharging current, the difference between internal maximum temperature, surface temperature and mean temperature are significantly high. Therefore, Richardson et al. [3] further extended the research and developed a thermalimpedance model by combining an EIS measurement at a single frequency with a surface temperature measurement for precise determination of internal temperature distribution. The fundamental steps in direct impedance measurement-based temperature estimation as presented by Richardson et al. [3] is shown in Figure 4.

The approach of Richardson et al. does not require knowledge of cell thermal properties, heat generation or thermal boundary conditions, however, the major limitation is the online impedance determination of each cell which is highly challenging. Moreover, uncertainties of environmental factors were not considered and a surface-mounted temperature sensor needs to be installed on each cell which is impractical so far. Whilst few approaches of online determination of impedance spectra across multiple frequencies using onboard power electronics of EVs have been reported [99], the application of these strategies in real-time temperature estimation has not yet been investigated. Furthermore, interpreting impedance measurements under superimposed DC currents is yet to be systematically investigated.

**Figure 4.** Fundamental steps in direct impedance measurement-based temperature estimation.

Online EIS-based temperature estimation strategy termed impedance-temperature detection (ITD) was proposed by Richardson and Howey [100] for sensorless temperature estimation which is adaptive to cell ageing and practical uncertainties. However, ITD cannot provide a general solution alone, thus, such a strategy combines surface-mounted sensors with ITD for accurate online temperature estimation [3]. Still, temperature sensors are required to be installed. Further to this study, they integrated ITD with an electricthermal model along with a DEKF for online core temperature estimation of a LIB cell even with unknown convection coefficient. They also demonstrated that the performance of the thermal model plus ITD is almost similar to the ITD with surface thermal sensors. Despite the advantages, the major limitations of the strategy are online impedance determination and the requirement of an accurate electric thermal model, thus encompassing the same drawback of conventional thermal modelling-based strategies. Moreover, although the strategy can estimate both core and surface temperature of an individual cell, the pack-level estimation strategy was not illustrated in this study.

The influence of cell temperature, SOC and SOH on the impedance spectrum, excitation frequency and thereby estimation accuracy of cell internal temperature was investigated by Zhu et al. [101]. Here, the temperature estimation was made based on an impedance response matrix analysis which was developed using EIS measurements. Despite high accuracy, the effect of the nonuniformity of the cell temperature and the correction method was not considered. Moreover, an extensive experimental study is required for modelling and the computational cost is also very high. Thus, the online application of the strategy is challenging. Identification of suitable frequency and other EIS parameters is very difficult whilst the estimation accuracy significantly depends on these parameters. Moreover, accurate determination of the real and imaginary parts of the impedance is highly challenging, whilst different decisions for these two parts leads to inaccurate temperature estimation. A combination of Linear Parameter Varying (LPV) thermal model and a polytopic observer-based battery-cell temperature estimation algorithm was proposed by Debert et al. [102]. The EIS-based strategy was also employed in references [3,103–106] to estimate the core temperature. Despite high accuracy, the major limitation is the determination of accurate impedance-temperature characteristics and it should be acquired in advance through tedious preliminary tests. In addition, the impedance-temperature characteristic of a cell is influenced by cell ageing leading to inaccurate prediction due to SOH deterioration. A summary of direct impedance measurement-based temperature estimation strategies is presented in Table 4.


**Table 4.** Summary of direct impedance measurement-based strategies.

#### *4.5. Machine Learning-Based Temperature Estimation*

With the overwhelming complexity of the electrochemical reactions inside the battery and the sensitivity of the battery parameters to the uncertainties of the working environment, the thermodynamic behavior varies significantly from the center region to the surface region. Most of the existing distributed thermal models and the lumped parameter thermal models are incapable to consider the spatiotemporal distribution of LIB packs, especially in the case of large-capacity battery packs. Moreover, it is highly difficult to represent these spatiotemporal dynamics by a single physics-based model. Here, the machine learning (ML) algorithms were widely employed to preserve the local dynamics to improve the modelling accuracy of nonlinear systems such as LIB. A schematic layout of the ML-based temperature estimation scheme is shown in Figure 5.

Liu and Li [107] employed a hybrid model of EECM and neural network (NN) based learning approach to develop a spatiotemporal thermodynamic model of LIB for accurate estimation of internal temperature distribution. The data-driven NN model used commonly measured signals of BMS to compensate for the model-plant mismatch caused by spatial nonlinearity and other model uncertainties. NN and support vector machine (SVM)-based [108] LIB temperature estimation strategy was investigated by Sbarufatti et al. [109]. A hybrid model of an radial basis function neural network (RBFNN) and EKF was employed by Liu et al. [110] to estimate the internal temperature of LIB. While they have considered the impact of temperature on cell behavior, the primary intention of these models was the estimation of SOC or SOH rather than estimating the cell temperature. One of the major challenges of pure ML-based strategies is the generalization capability. Feng et al. [111] developed an effective electrochemical-thermal-neural-network (ETNN) by fusing a lumped parameter electrochemical thermal, feed-forward neural network (FFNN) and a UKF. This method demonstrated appreciable performance in predicting the state of temperature (SOT) in a wide temperature range and large current conditions. However, the modelling is highly complex, the accuracy over different charging current/drive cycles was

not tested. Moreover, the computational efficiency and the suitability for online application are questionable. The back of the ETNN is the electrochemical model thus encompassing drawbacks similar to electrochemical models. In general, while ML-based schemes are computationally efficient, collecting training data and model training procedures are highly complex and time expensive. Moreover, real-life battery test data were not considered during ML-based model training in the existing literature; therefore, the accuracy of the existing ML-based strategies is still questionable. A summary of ML-based techniques reported by researchers is presented in Table 5.

**Figure 5.** Schematic layout of ML-based temperature estimation scheme.




**Table 5.** *Cont.*

#### *4.6. Magnetic Nanoparticles-Based Temperature Estimation*

The magnetization of Magnetic Nanoparticles (MNPs) is nonlinear under an ac magnetic field and the accurate temperature of MNPs could be estimated by using the ratio of the third and fifth harmonic response [112–114]. Further, the temperature sensitivity of MNPs with the increased DC magnetic field was studied by Zhong et al. [115]. They found that the temperature sensitivity of MNPs will decrease with an increased DC magnetic field. Further to this study, Zou et al. [116] developed an improved Magnetic nanoparticles thermometer (MNPT) for the core temperature estimation of LIB which works based on the temperature measurement of magnetic nanoparticles (MNPs). They also suggested the optimal range of the DC magnetic field strength to ensure maximum temperature sensitivity and minimum temperature error of the MNPT. It is noticed that this type of estimation topology is very bulky and costly. Moreover, the suitability of online prediction has not yet been assessed.

#### **5. Discussion on Issues, Challenges and Future Research Recommendations**

Temperature estimation schemes for LIBs can be designed with different levels of complexity depending on the requirement of accuracy level and detailing of the prediction results. Detailed model results and more accurate predictions are essential for safer and reliable operation of BMS. However, integrating more detailed cell phenomena into the model eventually increases the modelling complexity, computational cost while, at the same time, reduces the suitability for online prediction and low-cost onboard BMS. For instance, modelling complexity increases if the temperature gradient of each cell layer is considered instead of concentrated heat generation at the core. Secondly, the heat fluxes inside and outside the battery can be considered in both axial and radial directions instead of considering only the radial direction for simplicity. Furthermore, detailed models typically consider different heat transport modes, that is, conduction, convective and radiation whereas simplified models consider only conduction heat transfer. Integrating a greater number of phenomena in thermal modelling requires a lot of parameters, resulting in additional requirements of experimental measurements, modelling time and solid domain knowledge. In addition, very detailed and accurate information of cell structure, material properties and cell assembly are also needed. However, collecting this information from the cell manufacturer is highly challenging due to the confidentiality of the design data. Therefore, it can be inferred from the above discussion that the detailed models could produce highly accurate and complete insight into cell thermodynamics, however, their computational complexity may not be suitable for online prediction and onboard low-cost BMS. In general, most of the estimation strategies require measurements from physical sensors, however, installing a physical sensor at each cell is not practically possible as a highcapacity LIB pack consists of thousands of individual cells. Moreover, installing a sensor at the cell core for core temperature measurement is highly challenging. Several estimation schemes estimate the core temperature based on the surface temperature measurement. However, it is very erroneous as it takes a significant amount of time for the heat to reach the surface from the core. So far, most of the research studies have covered the temperature estimation scheme of a single LIB cell. Temperature estimation of a LIB pack is much more challenging. Thus, significant further research is recommended here. Moreover, the influence of fast charging/discharging on the cell temperature has not yet been deeply

explored. It is highly recommended to develop a health-conscious BMS. A summary of existing issues, challenges and future research recommendations to the research community are presented in Table 6.

**Table 6.** Summary of major issues, challenges and research recommendations.



**Table 6.** *Cont.*

#### **6. Conclusions**

This article presented a comprehensive review of the state-of-the-art temperature estimation strategies for lithium-ion batteries (LIBs) covering the necessity of an optimum estimation strategy, detailed discussion on the existing strategies, current issues, challenges and future research recommendations. It can be inferred that an accurate temperature estimation of LIBs is indispensable for effective thermal management, operational safety and several other crucial tasks of a Battery Management System (BMS). Measurement of each cell temperature using physical sensors is not practically possible, especially for a high-capacity battery pack consisting of thousands of individual cells. To develop an ideal temperature estimation scheme, one needs to concentrate on several factors, such as high accuracy, adaptability, small size, real-time estimation, distribution (to monitor the temperature gradient of the entire cell), low cost, and easily implementable for wide adoption. Typically, a temperature estimation scheme consists of a heat generation model and a heat transfer model. Depending on the modelling and computation strategies temperature estimation schemes can be grouped into six categories, namely, electrochemical model-based, equivalent electric circuit model (EECM)-based, machine learning (ML)-based, numerical analysis-based, direct impedance measurement-based, and magnetic nanoparticle-based. So far, numerical analysis-based schemes are most accurate followed by electro-chemical model-based schemes. However, both strategies have very high computational cost making them inappropriate for online prediction by a low-cost onboard BMS. Moreover, modelling complexity and experimental requirements are very high alongside the necessity of domain-specific knowledge. EECM-based schemes can be designed with different levels of complexity, accuracy level and computational cost. Simplified lower-order EECM-based schemes are extensively used in the literature and practice. Machine learning (ML)-based schemes are very promising due to their higher level of accuracy, ease of implementation and adaptability. In addition, reduced or even no requirement of equivalent modelling and domain experts. However, to obtain the feature vectors, very large volume and high-quality data are required which are typically very challenging to acquire. Here, a hybrid strategy combining an EECM and an ML is presumably a suitable solution. Direct impedance measurement and magnetic nanoparticle-based schemes are very newly developed. It is too early to assess their capability and suitability for online prediction and implementation in onboard BMS. Therefore, systematic guidelines about open research areas and future

research directions are highlighted in this study. It is also noticed that the majority of the research studies proposed temperature estimation schemes of a single LIB cell whereas temperature estimation of a LIB pack is much more challenging. Thus, significant further research is recommended here a well.

**Author Contributions:** Conceptualization, S.S.W.; methodology, A.S. and S.S.W.; investigation, A.S.; resources, S.S.W.; writing—original draft preparation, A.S.; writing—review and editing, A.S. and S.S.W.; visualization, A.S.; supervision, S.S.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

